"It won't be a be-all end-all sell signal, but new leadership in France could cause investor jitters that reverberate throughout global financial markets," said Detrick.

Hollande campaigned on the need to focus more on economic growth to reduce public debt, as opposed to austerity, which has been the main policy prescription for the three year-old European debt crisis.

While it remains to be seen to what extent Hollande will push his growth agenda, his countering approach causes concerns about how he might work with German Chancellor Angela Merkel, the key proponent of austerity.

Even so, many economists and market strategists say Hollande is likely to pursue policies that maintain fiscal discipline and will also make efforts to keep good relations with Germany.

While there could be some "initial friction with Merkel," Hollande will eventually form his own bond with the German leader, said Antonio Barroso, an analyst at political research firm Eurasia Group.

"Hollande is very pragmatic." said Barroso. "He knows that Germany is his most important partner. They will have to agree on a solution for the crisis."

What's more, there is not that much difference between many of the candidates' policies. Hollande and Sarkozy had both pledged to balance the nation's budget, although they differed on taxes, with Hollande pleding tax hikes on the rich.

"At the end of day, there's not a huge departure from the status quo," said Barroso.

Historically, May is the start of a weak period for the U.S. stock market, and the 'sell in May, and go away' phenomenon has reared its head for the past two years.

But Detrick doesn't expect the same type of weakness this year.

"I don't anticipate seeing the sizeable pullbacks that we saw during the last couple of years, but this is a time frame where the stock market rarely has explosive moves higher," he said.

Rather, Detrick expects the stock market to get through the economic and corporate news lull by largely moving sideways. Already, he notes, stocks are back at the levels they were about eight weeks ago.

And given that the market soared during the first three months of the year, "that's not necessarily a bad thing," he said.